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	<div align="center"><h1>A discrete valued time series model; <br>
	The polio dataset
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                     Code: <a href="polio.tpl">polio.tpl</a><br>
                     Data: 		<a href="polio.dat">polio.dat</a><br>
                     Initial values: <a href="polio.pin">polio.pin</a><br>
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                     All required files (DOS): <a href="polio.zip">polio.zip</a><br>
					 All required files (linux): <a href="polio.tar.gz">polio.tar.gz</a><br>					 
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                     Expected Results: <a href="polio.par">polio-expected-results.par</a><br><br>
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                     In a <a href="../admb_tutorial.html">DOS</a> window<br> 
					 Under <a href="../admb_tutorial.html">linux</a><br><br>
					 
					 Command line options:<br>
					 -ilmn 5<br>
					 -l1 10000000 -l2 100000000 <br>
					 -l3 10000000 -nl1 10000000
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             <font face="Arial, Helvetica" color="White"><b>Results: Computation times</b></font>
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                     ADMB-RE: 66 seconds.<br>
					 <A HREF="../citations.html#kuk:chen:1999">Kuk &amp; Cheng</A>: 3120 seconds.<br>
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<h3><strong>Model description</strong></h3>
As an example of a discrete valued time series we use the 'polio data' considered by <A HREF="../citations.html#kuk:chen:1999">Kuk &amp; Cheng (1999)</A>. 
It is assumed that <em>y<sub>i</sub></em> has a Poisson (<FONT FACE="Symbol">l</FONT><sub>i</sub>) distribution, where
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<div align="center">log(<FONT FACE="Symbol">l</FONT><sub>i</sub>) = <em><strong>X</strong><sub>i</sub></em><strong><FONT FACE="Symbol">b</FONT></strong> + <em>u<sub>i</sub></em>.</div> 
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Here, <em><strong>X</strong><sub>i</sub></em> is a covariate vector, <strong><FONT FACE="Symbol"> b</FONT></strong> is a vector of regression parameters 
and <em>u<sub>i</sub></em> is a first order autoregressive process<br>
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<div align="center"><em>u<sub>i</sub></em> = <FONT FACE="Symbol"> r</FONT>*<em>u<sub>i-1</sub></em> 
	+ <FONT FACE="Symbol"> e</FONT><sub><em>i</em></sub>.</div>
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Further details about the model can be found here: <a href="polio.pdf">polio.pdf</a>.
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